Theoretical solution for hydromagnetic convective flow over a continuously moving horizontal surface with uniform suction and internal heat generation/absorption is obtained. This represents a new class of boundary layer flow at a surface of finite length. The solutions for the velocity and temperature profiles are obtained for different parameters like Prandtl number, heat source parameter (α) and Hartmann number. It is observed that the velocity decreases considerably in the presence of magnetic field, as compared to its absence. The temperature increases in the presence of heat source and decreases in the presence of heat sink.